Nested_Stats_Sbar {pretest}

Predictive Accuracy Testing for Nested Environment SBar

Description

It calculates the SBar statistics for nested models with null hypothesis being the two models having equal predictive power following Pitarakis (2023). There are in total four versions of SBar, based on the assumptions of variance (homo or hete) and residuals (original or adjusted). All SBar statistics will be standarised to a standard N(0,1) normal distribution, and corresponding P values would be provided.

Usage

Nested_Stats_Sbar(Ehat1, Ehat2, lam20, tau0)

Arguments

Ehat1

Residual series from Model 1 (the smaller model). One dimension and numeric.

Ehat2

Residual series from Model 2 (the larger/nested model). One dimension and numeric.

lam20

Fraction of the sample used for Model 2, which should be within 0 and 1.

tau0

Fraction to determine the user-chosen range of lam10 over which the average is taken.

Value

A list of SBar statistics and corresponding P values will be produced. "adj" means a Clark and West's (2007) reformulation of sample MSE has been applied , and "NW" means robust Newey-West type estimator (c.f. Deng and Perron, 2008) for heteroskedastic errors has been used.

Author(s)

Rong Peng, [e-mail]

References

Pitarakis, J. Y. (2023). A novel approach to predictive accuracy testing in nested environments. Econometric Theory, 1-44.

Deng, A., & Perron, P. (2008). The limit distribution of the CUSUM of squares test under general mixing conditions. Econometric Theory, 24(3), 809-822.

Clark, T. E., & West, K. D. (2007). Approximately normal tests for equal predictive accuracy in nested models. Journal of econometrics, 138(1), 291-311.

See Also

Nested_Stats_S0

Examples

e1<- rnorm(15);
e2<- rnorm(15);
temp1 <- Nested_Stats_S0(e1,e2,lam10=0.5,lam20=0.8)
temp1$S_lam10_lam20_adj_NW     #\S^0_T(lam10, lam^20) with CW adjustment and NW correction
temp1$pv_S_lam10_lam20_adj_NW  #P value of it